1840.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



101 



ON TRUSSED BEAMS. 



Invuikd bij HeuJ! Laves of Haiwvir, nad befure ilw Riii/id tnslilulc uf 

 Briliah ./irchitecls, on Monday, March 20, 1640, by T. L. Donaldson', 

 Esq., Fellow. 



Mr. Laves took a beam of fir 40 ft. long and 91 in. deep, and 7a in. 

 wide, and supported at the ends. He gradually loaded it with 

 100 tbs. at a time, and found that when it had 1700tbs.it deflected 

 r>i in. He took a beam of the same dimensions and cut a horizontal slit 

 to within 3-G from each end, making the upper portion 5 inches deeper 

 anil the latter 4i ; he put iron straps at the ends, bound tightly round 

 to prevent tlie slit from extending — he then forced the upper and 

 lower part of the beam asunder by driving in blocks or wedges, until 

 they were as wide apart as half the depth of the beam -he supported 

 tlie beam at the ends and found that when he hud gradually loaded it 

 with ] 00 tbs. weight as before, until it bore 1700 lbs. it only deflected 

 o^ in., being 1?. less than the solid beam. He then separated the slit 

 apart Oi incbei or equal to the whole depth of the beam, and gradually 

 loaded it until it bore 17U0 tbs., wdien it deflected ili or 3 inches less than 

 the solid beam, and li less than the former. He then widened the 

 opening of the slit 13|, or equal to a depth of li of the solid beam, 

 and loaded it in hke manner with 1700 lbs., it deflected only 1^ inches, 

 being 4 inches less deflection than the solid beam. (See Fig. 1.) 



Figs. 1, 2, and 3. 



He then took pieces of fir 50 in. long, 2 in. deep, and 1 in. wide> 

 one was left solid, two others were slit so as to make the upper part 

 \\ inches deep, and the under | in., one piece having the slit half 

 the depth of the beam apart, the other J of the depth apart. See 

 fig. 2. 



It will be perceived that the principle of this system consists in the 

 combination of the two chief forces of materials, that is resistance to 

 compression, and resistance to tension. 



Resistance to compression is the one employed from the remotest 

 periods in the construction of arches and vaulting, and requires great 

 masses of materials ; and resistance to tension lias more lately been 

 employed, at least in Europe, for the construction of suspension bridges 

 by the application of chains, and requires less materials than the other 

 principle of compression, but frequently the insertion and use of chains 

 is obtained with difficulty, and produces vibrations and sensibly felt 

 undulations. 



These inconveniences have led to the application of this system. 

 It will be perceived that the under line or chain attached at the two 

 extremities of the upper curved line acts with positive force that of 

 tension, which is the greatest possible force of materials varying from 

 10 to 20,000 lbs. on the square inch of the transverse section in various 

 woods used in construction, and from 20 to 100,000 lbs. in metals. 



The upper line or beam acts by relative force that of compression, 

 and serves to prevent the lower line or chain from contracting the 

 two extremities. 



The lower line or chain hinders the upper line or beam from press- 

 ing out at the extremities. 



The supports and braces serve to unite the upper and lower lines or 

 beam and chain together, and then two forces neutralized form a com- 

 plete w hole, which sustains itself, and can neither thrust out nor draw 

 in. 



It is to be observed — 1st. That the force of the chain is dependent 

 upon the depth of the versed sine, and that the lower it is beneath the 

 horizontal line or chord of the arc the stronger it will bp. Arches of 

 solid construction require a rise of 20 or 15 ft. for the springing of the 

 arch to the soffit of the key stone, in a span of 100 ft; but the 

 chains in this system, if they have a rise or versed sine equal to 4 ft. 



2 in. in a span of 100 feet, the force of the chain reduces itself to one- 

 third of the absolute product — if the rise or versed sine equal (i ft. 



3 in. in the same span of 100 ft., the absolute force could be reduced 

 a half. 



Observe 2dly. That the upper line or beam, on account of the elasti 

 city (if llie materials, ought absolutely to have the convex form ae i 

 the diagrams, in order that when considerably loaded, the lengthenin 

 of the under line or chain by tension, and the shortening of the uppe 

 line or beam by compression, may not reduce the upper curved line to 

 an horizontal one, beneath which it would no longer serve by resistance 

 to the statical equilibrium of the construction. 



We observe, 3rdly, That the method of tying together the extremi- 

 ties of the curved lines will depend on the materials employed, and 

 must be calculated according to the weights that they will have to 

 bear. 



Such are the general principles of this system when applied in a 

 horizontal direction. 



We will now consider its application in a vertical or upright direc- 

 tion, and when used obliquely. 



It is obvious that the resistance of a story post or stay, wliether in 

 wood or metal, increases in a fixed proportion according to its thick- 

 ness. 



For tvood — the pieces of wood are sawn as before described with 

 one cut, or two cross cuts to within a certain length of the ends, and 

 these tied together by bolts or straps of iron. The cuts are then forced 

 apart by wedged blocks and kept in their places by bolts or straps of 

 iron. 



For iron — by connecting together at the ends, two or more bars of 

 iron, and separating the bars by wedges or pieces of iron, or iron 

 rings. 



The proportions and number of the dift'erent parts as chains, stays, 

 posts, &c., depend upon the purposes to which they may be applied, 

 and must of course be calculated accordingly by the architect. 



The most simple practical application of this systeui is for the pur- 

 pose of wooden bridges, and the upper line or beam may be materially 

 strengthened, and the combination stiftened by the introduction of 

 stays and braces. 



If the span of the bridge exceed the length of one beam, two may 

 be taken, sawn at one end only, and connected by two scarfing pieces, 

 into which they must be fitted with notches, and bolted or strapped 

 together so as to prevent their separating. — See fig. 3. 



In those parts where the ends of timbers abut upon any joints or 

 other timbers, it will be expedient to interpose thin plates of copper 

 or iron, in order to prevent the but ends from driving by the force of 

 compression into the beams, which would cause a sinking. 



For occasional purposes or military operations it may be useful to 

 adopt the same system applied to rough trees, which would even be 

 picturesque and useful in parks and gardens — and by connecting the 

 forked branches of two trees, to produce a combination which would 

 answer every purpose. 



For all the bridges hitherto described, it will be sulficient that the 

 versed sine of the lower arc or chain equal -yws o'" i-t of I'ls span. Thi's 

 is very moderate, for a beam requires -^±77 or ^ of the span, and bridges 

 or arches of masonry or solid construction, a rise of -^^ of the span. 



If the banks of a stream be too wide apart to admit the adoption of 

 this system in one span, it will be necessary to have intermediate piers 

 or columns, and to form a succession of framings tied together with 

 iron straps, or constructed in cast iron. 



If the bank of a river be too little elevated above high water mark, 

 or if it were requisite to give greater height in the middle of a series 

 of arches, in order to admit the ])assage of vessels, the lateral framings 

 admit of a gradual fall to the banks without affecting the stability of the 

 framing. 



Various bridges upon Mr. Laves principle have been constructed. 



1. One in oak at Hanover for foot passengers — the span 100 feet, 

 width 12 feet— cost about 112/. 



2. One in oak over the Nette river at Dernebourg, near Hildesheim — 

 span G<.) feet, breadth 15 feet, it being for carriages — cost about 70/. 



3. One in oak for foot passengers, and a water pipe at Dernebourg, 

 near Hildesheim — span 30 feet, breadth 10 feet — cost 26/. 



4. One in fir for foot passengers over the Eger at Elnbogen, in Bo- 

 hemia — length 36 feet, width 5 feet — cost 50s. 



5. One in fir for carriages over the Eger at Altsaltel, in Bohemia, 

 in two lengths, supported in the middle or junction of the two— total 

 length 125 feet, width 15 feet— cost about 100/. 



ti. One for carriages in wrought and cast iron, in the Royal Park of 

 Herrenhauson, near Hanover — length 83 feet width 20 feet — cost about 

 550/., comprising the wood paving for the carriage way. 



Besides others at Salzau, near Kiel, in the Royal Park at Hanover, 

 and one for the Count Munster at Dernebourg, near Hildesheim, vary- 

 ing from 22 to 42 feet span, and constructed in iron at a very moderate 

 cost, all of which are described in Mr. Laves' pamphlet. 



Figure 4 explains the construction of an iron bridge over a 

 river, the upper line consists of hollow cast iron cylinders united by 



